Answer: The required pattern is 13, 37, 109, 325, 973
Step-by-step explanation:
Since, each number in the sequence follows the following rule,
2 less than the 3 times of the previous number.
If we start from 5,
Then first number of the sequence = 3×5 - 2 = 15 - 2 = 13
Second number = 3× 13 - 2 = 39 - 2 = 37
Third number = 3× 37 - 2 = 111 - 2 = 109
Fourth number = 3×109 - 2 = 327 - 2 = 325
Fifth number = 3× 325 - 2 = 975 - 2 = 973
Hence, The required sequence is,
13, 37, 109, 325, 973
Factor −1/2−1/2 out of −1/2x+6.
To factor out -1/2 - 1/2 from -1/2x + 6, multiply -1/2 by the expression inside the parentheses and distribute. Then, simplify and combine like terms to get the factored form: -3/2x - 6.
Explanation:To factor out -1/2 - 1/2 from -1/2x + 6, you can rewrite the expression as (-1/2) * (x + 2(6)). Then, distribute to get (-1/2)x - (1/2)(2) * (x + 2(6)). Simplify further to get (-1/2)x - x - 6. Finally, combine like terms to get (-1/2 - 1)(x) - 6. Therefore, the factored form of the expression is -3/2x - 6.
Adina is constructing a line perpendicular to YJ . She has already constructed two arcs as shown. She moves her compass point to Y to construct an arc above the line. What must be true about the width of Adina’s compass opening before she draws the arc?
A. It must be narrower than it was when constructing the first two arcs. B. It must be the same as it was when constructing the first two arcs.
C. It must be wider than it was when constructing the first two arcs.
The arc is every two-point smooth curve. The length of an arc is called the length of its arc. In a chart, a chart arc is an adjacent pair of vertices. A semicircle is called an arc, whose endpoints lie on a circle diameter.
It must be broader than the first two arcs or you'll only get two circles alongside. The length of a point between the c and j is measured. The arches are a good way to cross.The compass shall be set to a length broader than the length of YC when drawing arcs below and above the YJ line.The arc production passes, not giving a line perpendicular to YJ.Therefore, the final answer is "Option C".
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complete the steps to demonstrate why you multiply by the reciprocal when dividing fractions. Find 1/4 divided by 3/8
The ice cream Palace received 3 gallons of strawberry ice cream, 5 pints of mocha ice cream, and 1 quart of vanilla ice cream today. How many pints of ice cream did they receive?
How long will it take for the object to fall all the way down to the ground? The function for objects dropped from a height where t is the time in seconds, h is the height in feet at time t, and h is the intial height is h(t)=-16t^2+h. The building is 162 feet tall.
Thanks so much!
Solve the equation for x. (Round your answer to three decimal places.) arctan(4x − 4) = -1
take the inverse arctan on both sides:
4x-4 = tan(-1)
4x-4 = -0.01745
4x = 3.98255
x = 3.9255 / 4
x = 0.996
the mean age of a dance troupe is 14.2 years. A 7-year-old sibling is invited to join the troupe. How does the sibling’s age affect the mean?
A. The new mean age will be 10.6 years.
B. The new mean age will be greater than 14.2 years.
C. The new mean age will be less than 14.2 years.
D. The new mean age will still be 14.2 years.
The new mean age will be less than 14.2 years.
What is mean?
There are several kinds of mean in mathematics, especially in statistics. For a data set, the arithmetic mean, also known as arithmetic average, is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.
According to questions, the mean age of a dance troupe is 14.2 years.
A 7-year-old sibling is invited to join the troupe.
We have to find how does the sibling’s age affect the mean.
There is no possible way to know how much the mean age decreases.
But the new mean age will decrease definitely.
Hence we can conclude that Option C is correct answer.
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Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→0 2x − sin(2x) 2x − tan(2x)
Using the L'Hospital's Rule, we differentiate the numerator and denominator of the given function separately, substitute these derivatives back into the function, and then attempt to evaluate the limit as x approaches 0.
Explanation:To find the limit of the given function as x approaches 0, we will use the L'Hospital's Rule since the function gets an indeterminate form 0/0 as x approaches 0. L'Hospital's Rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.
First, we differentiate the numerator and the denominator separately. For the numerator, the derivative of 2x is 2, and the derivative of sin(2x) is 2cos(2x). So the derivative of the numerator is 2 - 2cos(2x).
For the denominator, the derivative of 2x is 2, and the derivative of tan(2x) is 2sec²(2x), since the derivative of tan(x) is sec²(x) and because of the chain rule, we multiply by 2. So, the derivative of the denominator is 2 - 2sec²(2x).
Now, we substitute these derivatives back into the original function and take the limit as x approaches 0: lim x→0 (2 - 2cos(2x)) / (2 - 2sec²(2x)).
After further simplifying the above expression, you can evaluate the limit.
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The limit is 0.
We need to find the limit:
lim x→0 (2x − sin(2x)) / (2x − tan(2x))
Both the numerator and the denominator approach 0 as x approaches 0, which means it is in the indeterminate form 0/0. This suggests that we can use L'Hôpital's Rule.
According to L'Hôpital's Rule, we can differentiate the numerator and the denominator and then take the limit of the resulting fraction.
First, let's compute the derivative of the numerator:
Numerator: 2x - sin(2x)Derivative: 2 - 2cos(2x)Next, let's compute the derivative of the denominator:
Denominator: 2x - tan(2x)Derivative: 2 - 2sec²(2x)Now, we apply L'Hôpital's Rule:
lim x→0 (2 - 2cos(2x)) / (2 - 2sec²(2x))
As x approaches 0, cos(2x) approaches 1 and sec²(2x) also approaches 1, so:
lim x→0 (2 - 2(1)) / (2 - 2(1)) = 0 / 0
This fraction again gives an indeterminate form. Applying L'Hôpital's Rule a second time will be helpful. We need to differentiate the numerator and the denominator again:
Second derivative of the numerator: d/dx [2 - 2cos(2x)] = 4sin(2x)
Second derivative of the denominator: d/dx [2 - 2sec²(2x)] = -8sec²(2x)tan(2x)
Applying L'Hôpital's Rule once more, we get:
lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x))
Substitute x = 0:
lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x)) = 0
Therefore, the limit is 0.
What is the area of a regular polygon with 100 sides and a perimeter of 100 units?
Mira has breakfast at a restaurant. She leaves a 20% tip of $1.80. What is the price of Mira’s breakfast,before tip?
solve this system of linear equations. separate the x- and y- values with a coma. 6x+20y=-62
3x-9y=-12
To solve the system of linear equations, use the method of substitution by solving for one variable and substituting it into the other equation.
Explanation:To solve the system of linear equations:
6x + 20y = -62
3x - 9y = -12
We can use the method of substitution:
From the first equation, solve for x: x = (-62 - 20y) / 6Substitute the value of x into the second equation: 3((-62 - 20y) / 6) - 9y = -12Simplify and solve for y:After finding the value of y, substitute it back into the first equation to solve for x. The solution is: x = -2, y = 4.
G how many distinct ordered arrangements of the letters of the word boogaboo can be made?
The floor at a roller skating rink is 72.25 feet long and 51.5 feet wide how much longer is the rank than it is wide
for every 5 teachers there are 12 student. if there are a total 153 student and teachers how many teachers and student are present
5 +12 = 17
153 /17 = 9
9*5 = 45 teachers
9*12 = 108 studets
What are the values of the mean and standard deviation after converting?
What is 2 2/5 ÷ (- 1/4) And how?
The speed of the car was 45 mph. A driver noticed that while moving with this speed it took him 40 seconds to cross a bridge. On the way back crossing the same bridge, it took him 30 seconds. What was the speed of the car on the way back?
Answer:
Speed of car on the way back = 30 mph
Step-by-step explanation:
Speed of car on the way = 45 mph = 45 x 1.6 = 72 kmph = 20 m/s
Time taken to cross bridge on the way = 40 seconds
Length of bridge = Speed of car on the way x Time taken on the way = 20 x 40 = 800 m
Time taken to cross bridge on the way back = 30 seconds
Length of bridge = Speed of car on the way back x Time taken on the way back
800 = Speed of car on the way back x 30
Speed of car on the way back = 26.67 m/s =96 kmph = 30 mph
Speed of car on the way back = 30 mph
compute the following 8c2•5c2
The computation of 8C2•5C2 results in 280
The student asked: 'compute the following 8c2•5c2'.
We can solve this using the combinations formula, where nCr = n! / [r!(n-r)!].
Compute 8C2.-
8C2
= 8! / [2!(8-2)!]
= (8*7) / (2*1) = 28.
Compute 5C2.
5C2
= 5! / [2!(5-2)!]
= (5*4) / (2*1) = 10.
Multiply the results.
28 * 10 = 280.
Hence, the value of 8C2 • 5C2 is 280.
Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant.
The area of the plane 5x + 4y + z = 20 in the first octant is calculated using a double integral over the xy-plane. The limits are defined by the intersection of x and y with the xy-plane when z=0, and the solution is approximately 66.67 square units.
Explanation:To solve for the area of the part of the plane that lies in the first octant, we first need to isolate z in our equation. z = 20 - 5x - 4y. The limits for x and y in the first octant are from 0 to positive infinity, but in this case, they will be limited by the plane defined by z = 0 (the xy-plane). x and y will range from 0 to the point where they meet the plane. Therefore, we set z = 0 and solve for both x and y, giving us x = 4 and y = 5.
Now in order to calculate the area, we must interpret this integral on the xyz-plane as a double integral on the xy-plane. Now, we integrate over the region in the xy-plane that x and y range over:
Area = ∫ from 0 to 4 ∫ from 0 to (5 - 1.25x) (20 - 5x - 4y) dy dx
And that is the integral you need to calculate to find the area. Attempting to calculate this integral results in the area ≈ 66.67 square units.
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For which real numbers x and y is it true that x + y = x+y?
meredith bought 7 new t-shirts for $7.95 per shirt. if price included tax how much did she pay for all of the t-shirts? each step please
What happens to the average kinetic energy of water molecules as water freezes? A. It decreases as the water releases energy to its surroundings.
B. It increases as the water releases energy to its surroundings.
C. It increases as the water absorbs energy from its surroundings.
D. It decreases as the water absorbs energy from its surroundings.
Answer: Option (A) is the correct answer.
Explanation:
Kinetic energy is defined as the energy possessed by an object because of it's motion.
Whereas average kinetic energy is the sum of kinetic energy of all the particles of a substance.
Therefore, when water freezes then there will decrease in kinetic energy of particles and thus, particles will gain potential energy.
Hence, we can conclude that when water freezes average kinetic energy of water molecules decreases as the water releases energy to its surroundings.
The average "kinetic-energy" of water molecules decreases as water freezes, because water releases energy to its surroundings, option (a) is correct.
When water freezes, it undergoes a phase transition from a liquid to a solid state. During this process, water molecules lose energy and slow down, causing decrease in their average kinetic energy.
As temperature decreases, water molecules arrange themselves into a more structured pattern due to the formation of hydrogen bonds.
In order for water to freeze, it needs to release energy to its surroundings, in form of heat. This release of energy is necessary to facilitate transformation from a higher-energy liquid state to lower-energy solid state. As a result, average kinetic energy of water molecules decreases as water freezes.
Therefore, the correct option is (a).
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On a quiz worth 5 points, three students earned a 5, five students earned a 4, four students earned a 3,six students earned a 2 , nine earned a 1 and eight students earned a zero . What is the class average on this quiz
What operation extends this pattern? 100, 85, 70, 55... A) add 15 B) subtract 15 C) multiply by 15 Eliminate D) divide by 15
A local little league has a total of 85 players, of whom 80% are left-handed. How many left-handed players are there?
The question is asking us to find out how many players are left-handed from a total of 85 players, given that 80% of the players are left-handed. For this, we perform a simple calculation by finding 80% of 85, which equals 68. So, there are 68 left-handed players in the league.
Explanation:The subject of this question falls under the category of Mathematics, more specifically, it is about percentage calculations. In order to figure out how many left-handed players there are out of the total 85 players, we need to remember that percent means 'per 100'. So, 80% translates to 80 out of 100. Therefore, to find out how many are left-handed, we need to take 80% of 85.
The calculation is as follows:
Left-handed players = 85 * (80/100)
= 85 * 0.80
= 68
So, there are 68 left-handed players in the local little league.
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How to estimate 208 + 569
Find a line perpendicular to – 5 x – 4 y = 19 that passes through ( – 5 , 11 )
The product of 32 and an unknown number subtracted from 435 is 179 what is the value of the unknown number
Hello from MrBillDoesMath!
Answer: Case 1: approximately 429.4, Case 2: 8
Discussion:
Let the unknown be "x". The problem statement could mean either
32 * (435 -x) = 179 (#1)
or
435 - 32*x = 179 (#2)
It's unclear which one is wanted so we solve both of them.
----------------------------------------------#1
But for case #1
32 * (435 -x) = 179
32 * 435 - 32x = 179 or
13920 - 32x = 179
Add 32x to both sides
13920 = 179 + 32x
Subtract 179 from both sides:
13920 - 179 = 32x
Divide both side by x to get
x = (13920 -179)/32 = 13741/32 which is approximately 429.4
For case #2
----------------------------------------------#2
435 - 32x = 179. Add 32 x to each side
435 -32x + 32x = 179 + 32x. Subtract 170 from each side
435 -179 = 32x or
32x = 256 or x = 8
Regards, MrB
Mary made 1/8 of a batch of cookies in 1/10 pf an hour. How much time will she need to make 1 full batch of cookies?
Mary will need 48 minutes to make a full batch of cookies, as determined by setting up a proportion and then converting hours to minutes.
Mary made 1/8 of a batch of cookies in 1/10 of an hour. To find out how long it will take to make a full batch, we set up a proportion based on the information given. Since 1/8 of a batch takes 1/10 of an hour, we want to find out the time for 8/8 (a full batch), which is equivalent to 1.
Setting up the proportion, we can say that 1/8 of a batch is to 1/10 of an hour as 1 full batch (8/8) is to X hours:
1/8 batch : 1/10 hour = 1 batch : X hours
To solve for X, we multiply 1/10 by 8 because there are 8 parts of 1/8 in a full batch:
1/10 hour * 8 = 8/10 hours
Reducing the fraction 8/10, we get:
8/10 = 4/5 hours
To convert 4/5 of an hour to minutes, we multiply by 60:
4/5 hour * 60 minutes/hour = 48 minutes
Therefore, Mary will need 48 minutes to make 1 full batch of cookies.
A student has three mangos, two papayas, and two kiwi fruits. if the student eats one piece of fruit each day, and only the type of fruit matters, in how many different ways can these fruits be consumed
There are 210 different ways for the fruits can be consumed.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A student have 3 mangos, 2 papayas, and 2 kiwi fruits.
And, The student eats one piece of fruit each day, and only the type of fruit matters.
Now,
Total number of fruits = 3 + 2 + 2
= 7
And, There are 3 mangos, 2 papayas, and 2 kiwi fruits.
So, Number of ways for the fruits can be consumed, is calculated as;
= 7! / 3! 2! 2!
= 7 x 6 x 5 x 4 x 3! / 3! 2! 2
= 7 x 6 x 5 x 4 / 2 x 1 x 2 x 1
= 7 x 6 x 5
= 210
Thus, There are 210 different ways for the fruits can be consumed.
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